Optimal transportation problems with free Dirichlet regions

Giuseppe Buttazzo (1) , Edouard Oudet (2) , E. Stepanov (1)

1 Dipartimento di Matematica [Pisa]
2 Département de mathématiques

A Dirichlet region for an optimal mass transportation problem is, roughly speaking, a zone in which the transportation cost is vanishing. We study the optimal transportation problem with an unknown Dirichlet region S which varies in the class of closed connected subsets having prescribed 1-dimensional Hausdorff measure. We show the existence of an optimal Sopt and study some of its geometrical properties. We also present numerical computations which show the shape of Sopt in some model examples.

Domaines: Equations aux dérivées partielles [math.AP]

Giuseppe Buttazzo, Edouard Oudet, E. Stepanov. Optimal transportation problems with free Dirichlet regions. Progress in Nonlinear Differential Equations, 2002, 51 (51), pp.41--65. ⟨hal-00384991⟩